Question

Evaluate $1002 \times 998$ by using a special product.

Answer 1

Hint: In this problem, we have to simplify the given expression using a special product. We should first know that a special product is a mathematical term in which factors are combined to form products. It is called special because they do not need long solutions. We should know that the formula of a special product is multiplying \[\left( a+b \right)\] by \[\left( a-b \right)\]. We can now split terms into factors and simplify them.

Complete step by step solution:
Here, we have to evaluate \[1002\times 998\] by using a special product.
We should first know that a special product is a mathematical term in which factors are combined to form products. It is called special because they do not need long solutions.
We should know that the formula of a special product is multiplying \[\left( a+b \right)\] by \[\left( a-b \right)\].
We can now split the given expression in the form of multiplying \[\left( a+b \right)\] by \[\left( a-b \right)\], we get
\[\Rightarrow \left( 1000+2 \right)\times \left( 1000-2 \right)\]
We can now simplify the above step using the algebraic formula, \[{{a}^{2}}-{{b}^{2}}=\left( a+b \right)\left( a-b \right)\], we get
\[\Rightarrow {{\left( 1000 \right)}^{2}}-{{\left( 2 \right)}^{2}}\]
We can now simplify the above terms by squaring the terms and subtracting them, we get
\[\Rightarrow 1000000-4=999996\]
Therefore, the simplified answer of the given expression \[1002\times 998\] is 999996.

Note: We should always remember that the special product is a mathematical term in which factors are combined to form products. It is called special because they do not need long solutions. We should know that the formula of a special product is multiplying \[\left( a+b \right)\] by \[\left( a-b \right)\].